分野別セミナー

講演アブストラクト：
Conducting statistical inference on complex phenomena often requires making decisions between different model choices to explain the collected data. To facilitate such choices in the frequentist setting, information criteria are often used as estimators for models. In the Bayesian setting, analogs of such criteria are often proposed with the usual maximum likelihoods replaced by integrals of average likelihoods over estimated posterior measures. Such objects can typically be written as the integral of a random function with respect to a random measure. We use some generalizations of the Lebesgue dominated convergence theorem to obtain almost sure limits for such integrals to provide limits for some commonly used Bayesian model decision statistics. A Bayesian posterior consistency result is also presented to facilitate the simplification of some of these limits.